On light graphs in the family of 4-connected planar graphs

Authors:
Erhard Hexel
Affiliations:
Department of Mathematics, Ilmenau Technical University, PF 100565, D-98684 Ilmenau, Germany
Venue:
Discrete Mathematics
Year:
2002

Citing 5
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European Journal of Combinatorics - Special issue: Topological graph theory II

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Abstract

Let G be the family of all c-connected (c = 4 or 5) polyhedral supergraphs G of a given connected planar graph H where the minimum vertex degree of G is 5. Let R(H) denote the maximum face size of H. We have proved for all non-empty families G: In the case R(H) , every G ∈ G has a subgraph isomorphic to H whose vertices have a degree in G which is restricted by a number q = q(H,G). In the case R(H) ≥ c, such a restriction does not exist if H has a vertex of degree ≥ 5 or if H is 3-connected.